( 50 points!!) Mr. Brown is organizing a camping trip for the students in his scout troop. He has the following breakdown of how much it would cost him per day of the camping trip. Campground rental: $200 per day Training Cost: $20 per student per day Food Cost: $30 per student per day Miscellaneous Expenses: $50 per student per day Camping Gear Cost: $1,050 (one-time cost) Mr. Brown's total cost for organizing a 3-day camping trip with b students is represented by the expression below. Which statement best describes the coefficient of b?

A. It is Mr. Brown's total cost per day for campground rental and the camping gear.
B. It is Mr. Brown's daily cost per student for campground rental and the camping gear. C. It is Mr. Brown's daily cost per student, with training, food, and miscellaneous expenses.
D. It is Mr. Brown's total 3-day cost per student, with training, food, and miscellaneous expenses.

The perimeter of the triangle will be 41ft

The perimeter of a triangle is the sum of all the sides of the triangle

From the given triangle, we need to get the third sidee firse as shown:

h² = 12² + 12²

h² = 144 + 144

h² = 288

h = 17ft

Perimeter = 12 + 12 + 17

Perimeter = 41ft

Hence the perimeter of the triangle will be 41ft

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Answer: 41 ft

Step-by-step explanation:

Answer:

Send us a picture

Step-by-step explanation:

To find the missing dimension of a cone when the height is 4.2 and the volume is 3.6 cubed is to equate the general formula with the given information.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

To obtain the missing dimension of a cone we must equate the general formula for the volume of a cone to the given information.

Therefore, (1/3)πr²×4.2 = 3.6

(1/3)πr² = 0.86.

r² = 0.86/1.05.

r² = 0.82.

r = 0.9

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The gradient of the equation y=2x+3 is 2.

The Gradient (also called Slope) of a line shows how steep it is.

The gradient of a function is defined to be a vector field. Generally, the gradient of a function can be found by applying the vector operator to the scalar function. (∇f (x, y)). This kind of vector field is known as the gradient vector field.

Given equation: y = 2x + 3

y = mx + c

2x - y = -3

x/ -3/2 + y/3 = 1

Comparing both the equation we get,

m=2 (slope) and c=3(intercept)

So the gradient is 2.

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Tanya's car will go 10 2/5 miles on 1 gallon of gas.

What is expression?

An expression consists of one or more numbers or variables along with one more operation.

We can start by finding out how many quarters of gas are in a gallon. Since there are 4 quarters in a whole, there are 4 quarters in one gallon of gas. Therefore, we can find how many miles Tanya's car will go on 1 gallon of gas by multiplying the number of miles it goes on 1/4 of gas by 4:

2 3/5 miles ÷ (1/4) = 2 3/5 miles × 4 = 10 2/5 miles

So, Tanya's car will go 10 2/5 miles on 1 gallon of gas.

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Answer:

a couple different obes

Step-by-step explanation:

there are five

Answer:

(2, –3) is a solution to the system of linear equations.

Step-by-step explanation:

Given: Equations:

3x - y = 9 --------(1),

4x + y = 5 --------(2),

Add Equation (1) + Equation (2),

3x + 4x = 9 + 5

7x = 14  ( Combine like terms )

x = 2   ( Divide both sides by 7 ),

From equation 1:

3(2) - y = 9

6 - y = 9

-y = 9 - 6    ( Subtraction 6 on both sides )

-y = 3

y = - 3     ( Multiplying -1 on both sides )

Thus, the total length of lap covered to get the seven different obstacles is found as: 52 units.

the Pythagorean theorem is used to calculate the distance between two locations using the distance formula. The Pythagorean theorem can be rewritten as d = √((x2 - x1)²+(y2 - y1)²)  to calculate the separation between any two locations.

Given data:

Points on  y-axis and an x-axis are given,

M(-3,5), F(8,5), G(8,2), H(3,2), I(3,-5), J(-8,-5), K(-8,-2), and L(-3,-2).

Starting and ending point is F.

Points lies between the starting and ending are-

F ,G, H, I, J, K, L, M, F

Total length = sum of all length

d = √((x2 - x1)²+(y2 - y1)²)

FG =  √((8 - 8)²+(2 - 5)²)

FG =  √9

FG =  3

GH =  √((8 - 3)²+(2 - 2)²)

GH  =  √25

GH =  5

HI =  √((3 - 3)²+(2 + 5)²)

HI  =  √49

HI  =  7

IJ =  √((3 + 8)²+(-5 + 5)²)

IJ =  √121

IJ =  11

JK =  √((-8 + 8)²+(-2 - 5)²)

JK =  √9

JK =  3

KL =  √((-8 + 3)²+(-2 + 2)²)

KL =  √25

KL =  5

LM =  √((-3 + 3)²+(-2 - 5)²)

LM =  √49

LM =  7

MF =  √((8 + 3)²+(+5 - 5)²)

MF =  √121

MF =  11

Total length = 3 + 5 + 7 + 11 + 3 + 5 + 7 + 11

Total length = 52 units

Thus, the total length of the lap covered to get the seven different obstacles is found as: 52 units.

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Answer:

\(3x + 15 = 4x + 12 \\ 4x - 3x = 15 - 12 \\ \boxed{x = 3}\)

Answer:

  walk area = 125.6 m²

Step-by-step explanation:

You are asked for the area of a sidewalk of given width that is around a circle of given radius. The pattern you're asked to fill in would have you compute the area of the inner circle, and of the outer circle, then find the difference between the areas.

__

The formula for the area of a circle is ...

  A = πr²

The radius is shown as 11 m, so its area is ...

  A = π(11 m)² = 121π m² = 379.94 m²

The radius is shown as 9 m, so its area is ...

  A = π(9 m)² = 81π m² = 254.34 m²

The difference between the two areas is ...

  walk area = big circle area - small circle area

  walk area = 379.94 m² -254.34 m² = 125.6 m²

_____

Additional comment

The area can also be computed by multiplying the centerline length of the sidewalk by its width. The center of the walk is (9+11)/2 = 10 m from the centers of the circles, so the circumference (centerline length) is

  C = 2πr = 2(3.14)(10 m) = 62.8 m

The width of the sidewalk is 11 -9 = 2 meters, so its area is ...

  (2 m)(62.8 m) = 125.6 m² . . . . sidewalk area

Answer:B is correct

Step-by-step explanation:

i did the lesson

Answer:

I think it's -35

Step-by-step explanation:

sorry if its wrong

Answer:

1) w=

2) w= -8/9

3) y= -12

Step-by-step explanation:

Can you rewrite the 1st problem or take a picture of it? I don't understand how I would write that haha. You’re welcome :)

The three solutions of the equation y = -2x - 1 are (–2, 3), (1, –3), and (2, –4).

To find the solutions, we substitute different values of x into the equation and solve for y.

For the first solution, when x is –2, we have y = -2(-2) - 1 = 3. Therefore, the first solution is (-2, 3).

For the second solution, when x is 1, we have y = -2(1) - 1 = -3. Thus, the second solution is (1, -3).

For the third solution, when x is 2, we have y = -2(2) - 1 = -4. Hence, the third solution is (2, -4).

These three points satisfy the equation y = -2x - 1, and therefore, they are the solutions of the equation. They represent coordinate pairs (x, y) where the equation holds true.

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Step-by-step explanation:

let a be the first term

x be the increment

2nd term will be a+x

3rd term will be a+2x

so 25 th term = a+24x= 135

11th term

a+10x = 3(a+x)

a = 7/2 x

solve this in 25th term

x = 10

a= 35

sum of 100 terms

s= n/2(35+1025)

1025 is the 100th term and n = 100

s = 53000

nth term

35+10(n-1)

Answer:

Step-by-step explanation:

continuous

increasing then decreasing

As of the given condition graph must be increasing and then decreasing. Option C is correct.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
As mentioned in the question,

On the coordinate plane, a curve starts in quadrant 2, up to the y-axis, and then decreases into quadrant 1. Implies that curve first increases and then decreases.

Thus, As of the given condition graph must be increasing and then decreasing. Option C is correct.

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Answer:

you can use compass to make straight line

Answer:

B. 8.66

Step-by-step explanation:

y = 6(1.13)^x

x = 3 so it is:

y = 6(1.13)^3

Using the rules of PEDMAS or BADMAS

We see that parenthesis and exponents must always be calculated first, so we calculate 1.13^3 first:

y = 6 * (1.443)

y = 8.66

Hope this helped!

Answer:

c

Step-by-step explanation:

Using the z-distribution, the sample sizes required are given as follows:

a) 822.

b) 1068.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

Then, the margin of error is given by:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

We have a 95% confidence level, hence\(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

Item a:

The estimate is of \(\pi = 0.26\), hence we solve for n when M = 0.03.

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.03 = 1.96\sqrt{\frac{0.26(0.74)}{n}}\)

\(0.03\sqrt{n} = 1.96\sqrt{0.26(0.74)}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.26(0.74)}}{0.03}\)

\((\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.26(0.74)}}{0.03}\right)^2\)

n = 821.2

Rounding up, a sample of 822 is needed.

Item b:

No prior estimate, hence \(\pi = 0.5\), which is when the largest sample size is needed.

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.03 = 1.96\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.03\sqrt{n} = 1.96\sqrt{0.5(0.5)}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.03}\)

\((\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.03}\right)^2\)

n = 1067.11

Rounding up, a sample of 1068 is needed.

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The solution set {(-4, 2)} is satisfied when C = 3 and D = -4. Hence, the correct answer is option C.

To find the values of C and D that satisfy the given system of equations, we substitute the coordinates of the solution set {(-4, 2)} into the equations and solve for C and D.

Substituting x = -4 and y = 2 into the first equation, we have:

C(-4) - 2(2) = -16

-4C - 4 = -16

-4C = -12

C = 3

Next, substituting x = -4 and y = 2 into the second equation, we have:

2(-4) + D(2) = -16

-8 + 2D = -16

2D = -8

D = -4

Therefore, the values of C and D that satisfy the system of equations and yield the solution set {(-4, 2)} are C = 3 and D = -4. Thus, the correct answer is option c: C = 3, D = -4.

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The transformation that map Circle X onto Circle Y:

1) Translation by the vector  < - 4, 5 >.

2) Dilation by a scale factor of 3/4.

The correct options are C and D.

A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation may alternatively be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

Given:

Two circles centered at X and Y.

Center of circle X: (-5, 6)

Center of circle Y: (-1, 1)

The translation:

< -1, 1 > = < -1 -4, 1 + 5 >

We get the center of Y.

So, the translation is < - 4, 5 >.

Now the dilation by a scale factor 3/4.

Therefore, the translation is < - 4, 5 >.

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The behavior of the graph of a polynomial function when the leading coefficient of an odd degree polynomial is greater than zero is the polynomial's final behavior will be "down" on the left and "up" on the right.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1. Expressions that contain variables of various intensities, non-zero coefficients, positive exponents (of variables), and constants are known as polynomial functions. For instance, the polynomial in "b" of degree 2 is f(b) = 4b² - 6.

Given,

The behavior of the graph of a polynomial function when the leading coefficient of an odd degree polynomial is greater than zero is:

This odd-degree polynomial's end behavior will resemble that of a positive cubic because its leading coefficient is positive. As a result, the polynomial's final behavior will be "down" on the left and "up" on the right.

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The monthly rate for the given loan is 1.0118%.The annual rate for this loan is 12.1423%.

Given loan: $150,000

Payment per month: $1,770

Duration of loan: 10 years

Interest = ?

The formula for monthly payment is given by:

\(PV = pmt x (1 - (1 + r)^-n) / r\)

Where, PV is the present value, pmt is the payment per period, r is the interest rate per period and n is the total number of periods.Solving the above formula for r will give us the monthly rate for the loan.

r = 1.0118%The monthly rate for the given loan is 1.0118%.The annual rate can be calculated using the following formula:

Annual rate = \((1 + Monthly rate)^12 - 1\)

Annual rate = 12.1423%

The annual rate for this loan is 12.1423%.The effective annual rate can be calculated using the following formula:

Effective annual rate =\((1 + r/n)^n - 1\)

Where, r is the annual interest rate and n is the number of times interest is compounded per year.If interest is compounded monthly, then n = 12

Effective annual rate = (1 + 1.0118%/12)^12 - 1

Effective annual rate = 12.6801%

The effective annual rate for this loan is 12.6801%.

Total amount paid after 10 years = Monthly payment x Number of payments

Total amount paid after 10 years = $1,770 x 120

Total amount paid after 10 years = $212,400

The total amount paid after 10 years is $212,400.

The future value for this loan can be calculated using the following formula:

FV = PV x (1 + r)^n

Where, PV is the present value, r is the interest rate per period and n is the total number of periods.If the loan is paid off in 10 years, then n = 120 (12 payments per year x 10 years)

FV = $150,000 x (1 + 1.0118%)^120

FV = $259,554.50

The future value for this loan is $259,554.50.

Thus, the monthly rate for the loan is 1.0118%, the annual rate for this loan is 12.1423%, the effective annual rate for this loan is 12.6801%, the total amount paid after 10 years is $212,400 and the future value for this loan is $259,554.50.

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